A simplified fuzzy model to mimic a nonlinear system, applied to a plasma source

This paper develops a fuzzy model to simulate the behaviour of a nonlinear system, in particular a plasma source, with a view to developing a control system for processing plasmas employing a helicon source. Genetic algorithms are employed to optimize fuzzy rules related to the parameters of the fuzzy model which contain a set of variable zeros and poles of the nonlinear system as well as its time delay. A practical application of the fuzzy model is to estimate the electron number density of a low-temperature plasma. Based on the membership functions of the input and output, a set of fuzzy rules by which the variable zeros and poles are identified is derived and optimized using a genetic algorithm. The principal reason for investigating the proposed fuzzy model is the subsequent computer-aided design of a fuzzy controller to control the nonlinear system. Two experimental results are presented to validate the fuzzy model method. One shows a computer simulation and the other predicts the real-time behaviour of the plasma source as its input parameters are varied.